Linearity preserving modified LDA methods for unsteady advection-diffusion problems

The developments of linearity preserving (LP) residual distribution (RD) schemes for unsteady hyperbolic and hyperbolic-parabolic equations are presented. This is achieved by utilizing a classical aerodynamics philosophy on the standard finite-element technique to modify classic RD schemes such as LDA to be truly LP even for unsteady advection-diffusion cases using an explicit time integration. The new approach herein would also highlight what previous analytical approaches lacked.

Automated summary

This study presents the developments of linearity preserving (LP) residual distribution (RD) schemes for unsteady hyperbolic and hyperbolic-parabolic equations. By modifying classic RD schemes such as LDA using an explicit time integration and utilizing a classical aerodynamics philosophy on the standard finite-element technique, the new approach achieves true LP even for unsteady advection-diffusion cases and addresses the limitations of previous analytical approaches.